A158784 Expansion of (1+4*x+14*x^2)/(1-2*x^2-64*x^3).

1, 4, 16, 72, 288, 1168, 5184, 20768, 85120, 373312, 1499392, 6194304, 26890752, 108349696, 450216960, 1937707520, 7834814464, 32689300480, 139682910208, 566806726656, 2371481051136, 10073319706624, 41018592608256

Offset

0,2

Comments

Can be generated by multiplying the sum of the top row of the n-th power of the matrix [ (0,2,0), (0,0,2), (2,1/4,0)] by 2^n.

Links

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (0,2,64).

Formula

a(n)= 2*a(n-2) +64*a(n-3). [From R. J. Mathar, Mar 31 2009]

Mathematica

Clear[M, v, t, n];
M = {{0, t, 0}, {0, 0, t}, {t, 1/t^2, 0}};
v[0] = {1, 1, 1};
v[n_] := v[n] = M.v[n - 1];
CharacteristicPolynomial[M, x];
t = 2;
a = Table[t^n*v[n][[1]], {n, 0, 30}]
LinearRecurrence[{0, 2, 64}, {1, 4, 16}, 30] (* Harvey P. Dale, Apr 05 2019 *)

Crossrefs

Sequence in context: A224660 A330610 A327541 * A180141 A226282 A013991

Adjacent sequences: A158781 A158782 A158783 * A158785 A158786 A158787

Keyword

nonn

Author

Roger L. Bagula, Mar 26 2009

Status

approved